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Approximate and pseudo-amenability of various classes of Banach algebras

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Approximate and pseudo-amenability of various classes of Banach algebras. / Choi, Yemon; Ghahramani, Fereidoun; Zhang, Yong.

In: Journal of Functional Analysis, Vol. 256, No. 10, 15.05.2009, p. 3158-3191.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Choi, Y, Ghahramani, F & Zhang, Y 2009, 'Approximate and pseudo-amenability of various classes of Banach algebras', Journal of Functional Analysis, vol. 256, no. 10, pp. 3158-3191. https://doi.org/10.1016/j.jfa.2009.02.012

APA

Choi, Y., Ghahramani, F., & Zhang, Y. (2009). Approximate and pseudo-amenability of various classes of Banach algebras. Journal of Functional Analysis, 256(10), 3158-3191. https://doi.org/10.1016/j.jfa.2009.02.012

Vancouver

Choi Y, Ghahramani F, Zhang Y. Approximate and pseudo-amenability of various classes of Banach algebras. Journal of Functional Analysis. 2009 May 15;256(10):3158-3191. https://doi.org/10.1016/j.jfa.2009.02.012

Author

Choi, Yemon ; Ghahramani, Fereidoun ; Zhang, Yong. / Approximate and pseudo-amenability of various classes of Banach algebras. In: Journal of Functional Analysis. 2009 ; Vol. 256, No. 10. pp. 3158-3191.

Bibtex

@article{ec3a24bddfc34bf9aa06ccdf1a7a9bf2,
title = "Approximate and pseudo-amenability of various classes of Banach algebras",
abstract = "We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ℓ1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups.",
keywords = "Amenable Banach algebra, Amenable group, Approximately amenable Banach algebra , Approximate diagonal , Approximate identity , Fourier algebra , Segal algebra , Semigroup algebra , Reduced C∗-algebra",
author = "Yemon Choi and Fereidoun Ghahramani and Yong Zhang",
year = "2009",
month = may,
day = "15",
doi = "10.1016/j.jfa.2009.02.012",
language = "English",
volume = "256",
pages = "3158--3191",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "10",

}

RIS

TY - JOUR

T1 - Approximate and pseudo-amenability of various classes of Banach algebras

AU - Choi, Yemon

AU - Ghahramani, Fereidoun

AU - Zhang, Yong

PY - 2009/5/15

Y1 - 2009/5/15

N2 - We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ℓ1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups.

AB - We continue the investigation of notions of approximate amenability that were introduced in work of the second and third authors together with R.J. Loy. It is shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable. Further examples are obtained of ℓ1-semigroup algebras which are approximately amenable but not amenable; using these, we show that bounded approximate contractibility need not imply sequential approximate amenability. Results are also given for Segal algebras on locally compact groups, and algebras of p-pseudo-functions on discrete groups.

KW - Amenable Banach algebra

KW - Amenable group

KW - Approximately amenable Banach algebra

KW - Approximate diagonal

KW - Approximate identity

KW - Fourier algebra

KW - Segal algebra

KW - Semigroup algebra

KW - Reduced C∗-algebra

U2 - 10.1016/j.jfa.2009.02.012

DO - 10.1016/j.jfa.2009.02.012

M3 - Journal article

VL - 256

SP - 3158

EP - 3191

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 10

ER -